Modified Henderson Equation Research Articles

THIN?LAYER DRYING RATES, STRESS CRACKING, AND DIGESTIBILITY OF SELECTED HIGH?OIL CORN HYBRIDS

ThinClayer drying tests were conducted on samples of five highCoil corn hybrids harvested from a private plot in1997. Samples were dried at temperatures ranging from 38C to 104C, dewCpoint temperature of 19C, and airflow rate of7.2 m 3 /min. Corn was dried from initial moisture contents of 20.2% to 20.9% w.b., to final moisture contents of approximately15% w.b. Half of the sample from each drying temperature was cooled rapidly with 4C forced air, and half was temperedfor one hour before cooling to room temperature nonCevaporatively in sealed plastic bags. Stress cracks were counted on100 kernels from each sample. Differences in stressCcrack indices between hybrids due to drying and cooling treatmentsranged from 22% to 34%. Equilibrium moisture content was calculated using the modified Henderson equation. Finalmoisture ratios were then used to estimate drying rates. Hybrid differences in drying rates of 10% to 15% were observed.Digestibility tests with ducks were performed on samples of a single hybrid from each drying temperature. Apparentmetabolizable energy, apparent nitrogen retained, and dry matter retained were analyzed. No significant differences indigestibility between drying temperatures were detected with the hybrid that was tested.

PH—Postharvest Technology: Comparison of Seven Equilibrium Moisture Content Equations for some Medicinal and Aromatic Plants

In this research, seven equilibrium moisture content (EMC) and equilibrium relative humidity (ERH) equations (modified Henderson, Chung–Pfost, Modified Halsey, Henderson, Chen–Clayton, Iglesias–Chirife and modified Oswin) are compared on their ability to fit data for some medicinal and aromatic plants. Thirteen data sets comprising 13 plants are used. Comparisons are based on standard error of estimate, coefficient of determination, residual sum of square and residual plots. Both the modified Halsey and the modified Oswin equations were found as the most versatile models to accurately describe the equilibrium moisture content and equilibrium relative humidity (EMC/ERH) relationships for medicinal and aromatic plants. The modified Henderson equation is a good model for fennel and cinnamon. The Chung–Pfost equation is suitable for muscat, coriander, ginger and cinnamon. The Iglesias–Chirife, Henderson and Chen–Clayton equations are among the least successful models for medicinal and aromatic plants, respectively.

Thin layer Drying Rate and Loss of Viability Modelling for Rapeseed (Canola)

For the drying process and safe storage of rapeseed, the experimental equilibrium moisture content and the thin layer drying curves for rapeseed (Brassica napus L.), variety Hyola-401, were determined; and the effect of drying air temperature and relative humidity on seed quality was evaluated. The equilibrium moisture content curves were obtained, both experimentally and by fitting the modified Henderson equation to the experimental data, using non-linear regression. The same procedure was used to fit the Page thin layer drying equation to the thin layer drying experimental data. The results showed that both, the modified Henderson and the Page equations describe adequately the variation of equilibrium moisture content and thin layer drying rates, respectively, as a function of drying air temperature and relative humidity. It was also observed that the drying air temperature and relative humidity affect significantly the vigour and germination of rapeseed, showing that the drying conditions is a crucial factor for maintaining the physiological quality of the seeds.

MOISTURE SORPTION CHARACTERISTICS OF FREEZE-DRIED, OSMOFREEZE-DRIED, AND OSMO-AIR-DRIED CHERRIES AND BLUEBERRIES

Equilibrium moisture contents (EMC) of freeze-dried, osmo-freeze-dried, and osmo-air-dried sweet cherries(Bing) and highbush blueberries (Bluecrops) at 10, 25, and 40C were determined by equilibrating samples to eightdifferent humidities. Moisture sorption isotherms of cherries and blueberries displayed characteristics typical of highsugarfoods with crossing points at 0.4 to 0.8 water activity (aw) depending on temperature. Fitting of five sorptionmodels (modified Henderson, Chung-Pfost, Halsey, Oswin, and Guggenheim-Anderson-de Boer) to data showed that themodified Henderson equation predicted isotherms with the smallest standard error of moisture content and mean relativepercent error values. None of the equations described the EMC data adequately for the entire range of ERH. The modifiedHenderson equation was found to give a good fit at aw < 0.8. For aw < 0.5, the modified Oswin and Halsey equationsgave acceptable results. However, the Halsey equation was the best model for aw > 0.8.

EQUILIBRIUM MOISTURE CONTENT OF DRIED BLOOD FLOUR FN THE TEMPERATURE RANGE OF 20 - 50°C

ABSTRACT The paper presents results of water sorption tests of dried blood flour carried out tinder laboratory conditions and mathematical analyses of sorption isotherms obtained. Moisture equilibrium data were investigated at air temperatures in the range of 20–50°C and water activity ranging from 0 4 to 0 99. The experimental procedure used was a gravimetric dynamic method with continuous registration of sample weight changes. Sorption capacity decreases as temperature increases. Rehydration of the dried material results in hysteresis but this phenomenon was small. Four models of equilibrium moisture content/equilibrium relative air humidity (Chung—Pfost. Halsey. Henderson, and Oswin) were evaluated for their ability to fit data for the samples of dried blood. The modified Henderson equation was a good model for moisture adsorption and desorption of dried blood flour

Relationship between body size, fill volume, and mass transfer area coefficient in peritoneal dialysis.

A peritoneal dialysate fill volume of 2 L has become the standard of clinical practice, but the relationships between body size, fill volume, and mass transfer area coefficient (KoA) have not been well established. These relationships were studied in 10 stable peritoneal dialysis patients who underwent six peritoneal equilibration studies (2 h each) at fill volumes of 0.5, 1, 1.5, 2, 2.5, and 3 L. The concentration-time profiles for urea, creatinine, and glucose were measured at each fill volume, and residual volumes were calculated from the preceding dwell period. A modified Henderson equation was used to calculate the KoA for the three solutes as a function of fill volume. By normalizing the KoA for each solute to the value at 2 L, the data for all three solutes collapsed onto the same trend line when plotting the normalized KoA versus dialysate volume. Between 0.5- and 2-L fill volumes, the average normalized KoA increases in an almost linear fashion, its value almost doubling over this range. Between 2- and 3-L fill volumes, there is less than a 10% change in the normalized KoA. However, fill volumes for peak urea KoA were found to increase with increasing body surface area (R = 0.76), being around 2.5 L for an average-sized patient and increasing to between 3 and 3.5 L for body surface areas > 2 m2. To maximize solute transport, these relationships between body size, volume, and KoA should be considered when choosing fill volumes for continuous ambulatory peritoneal dialysis and automated peritoneal dialysis and when deciding reserve and tidal volumes for tidal peritoneal dialysis.

MODELING OF WATER ACTIVITY AND ENTHALPY OF WATER SORPTION IN CASSAVA CHIPS

Abstract The Guggenheim-Anderson-de Boer (G.A.B.) and modified Henderson equations adjusted by linear and non-linear regression were used for mathematical description of sorption isotherms of yuca. The highest result of generalized correlation coefficient was obtained by the G.A.B. direct nonlinear regression. Weighted linear regression of results for isosteric heat sorption must be employed to fit the Clausius-Clapeyron equation.

The Moisture Content/Relative Humidity Equilibrium Relationship Of Wheat - A Review

ABSTRACT Thirty three sources of hygroscopic data for wheat are identified. Gravimetric methods predominate in the literature, followed by hygrometric methods which largely employ a dew Point technique for relative humidity determination. Hysteresis effects vary considerably in magnitude. The greatest difference between adsorption and desorption isotherms occurs in the 20–40% RH region. A table of equilibrium moisture contents interpolated from the data sets is presented for a Fixed set of temperatures and RH to enable comparison. The isotherm equations used to fit the data are also revewed. The Strohman-Yoerger, Modified-Oswin, Modified-Chung-Pfost, Chen-Clayton and Modified-Henderson equations are identified as the most suitable. Further investigation is needed to compare them.

Moisture sorption behaviour of mineral acid, lactic and rennet caseins in the temperature range 27–80 °C

SummaryThe moisture desorption isotherms of mineral acid, lactic and rennet caseins were determined at ˜ 28, 55 and 80 °C. The isotherms were all sigmoid type II according to the BET (Brunauer et al. 1938) classification. A modified Henderson equation was found best to describe the relationship of equilibrium moisture content, water activity (aw) and temperature for all three types of casein. BET monolayer moisture contents and heats of desorption of the three types of casein were calculated. Equilibrium moisture contents at aw 0·432 and 30 °C for mineral acid casein made under a range of manufacturing conditions varied significantly depending on the drying conditions. More severe drying conditions produced lower equilibrium moisture contents.

ADSORPTION EQUILIBRIUM MOISTURE CONTENTS OF LONG-GRAIN ROUGH RICE

ABSTRACT The effects of temperature, relative humidity, and initial moisture content on equilibrium moisture content of long-grain rough rice under adsorptive conditions were investigated. Air temperatures of 12.5, 15, 20, and 30 C, relative humidities of 70, 80, and 90%, and initial moisture contents ranging from approximately 9% to 15% w.b. were used to obtain equilibrium moisture content data. For a given air condition, equilibrium moisture content varied linearly with initial moisture content. A difference of one percentage point in equilibrium moisture content was measured when rice samples at initial moisture contents of 9% and 15.5% were equilibrated to an air condition of 30 C and 90% relative humidity. Equations were developed to relate equilibrium moisture content to initial moisture content, temperature and relative humidity. The Modified Henderson and Chung equations were modified to include the contribution of initial moisture content in predicting equilibrium moisture content.

Equilibrium Moisture-Equilibrium Relative Humidity Relationship for Canola Meal

ABSTRACT THE desorption isotherms of canola meal were measured by bringing a small amount of air to equilibrium with the canola meal sample in a closed loop experimental unit. The equilibrium relative humidities (ERH) were measured for the canola meal samples at 5.0, 7.5, 10.0, 12.5, 15.0 and 17.5% moisture contents wet basis (wb) and 10, 20, 30, 40 and 50C temperatures. The effect of temperature on the ERH was minimal at the moisture contents below 15% wb. At higher moisture contents, increase in the temperature resulted in a noticeable increase in the equilibrium relative humidity. A non-linear regression was performed to estimate the constants of the modified Henderson and the Chung-Pfost equations. At moisture contents of 5% wet basis, neither equation described the equilibrium relative humidity with accuracy. The modified Henderson equation described the data better in the humidity range from 20% to 80%.

Equilibrium Moisture Relations for Pine Shavings Poultry Litter Material

ABSTRACT EQUILIBRIUM moisture measurements were made for clean pine shavings poultry litter material at 20 and 26 C for a wet basis moisture content range of 1.3 to 30.7%. Parameters were estimated for the Chung and Modified Henderson equations for predicting both equilibrium moisture content and equilibrium relative humidity. Temperature was not included as a variable due to data scatter. There was little difference in the ability of each equation to represent the data. Attempts at measurements on shavings-manure mixture were unsuccessful.

Equilibrium Relative Humidity-Moisture Content of Rapeseed (Canola) from 5 °C to 25 °C

ABSTRACT -EQUILIBRIUM moisture contents of rapeseed (canola) variety Tobin Brassica Campestris for environmental conditions in the range of 5 C to 25 C were determined. The experimental data were in good agreement with the published data for other varieties. A non-linear regression was performed to estimate the constants of the modified Henderson equation and of the Chung equation. Both equations had a similar fit to the data up to 85% relative humidity. The modified Henderson equation had slightly smaller sum of squares of residuals. It was concluded that either equation represents the equilibrium relative humidity-moisture content relationship up to 85% relative humidity. For calculations above 85%, the modified Henderson equation is preferred until more experimental data to cover a wider range of relative humidity are produced

MATHEMATICAL MODELING OF HEAT AND MOISTURE TRANSFER-RELATED PROPERTIES OF INTERMEDIATE MOISTURE APPLIES

Mathematical models for heat and moisture transfer-related properties of intermediate moisture apples were developed. The models of thermal properties were based on a linear dependence of thermal conductivity on temperature and moisture content, a logarithmic dependence of bulk density on moisture content, and a linear dependence of specific heat on moisture content. The effect of moisture content and temperature on moisture diffusivity was modeled by an exponential relationship. The sorption data were adequately fitted by the Modified Henderson's equation.

Equilibrium Moisture Properties of Corn Cobs

ABSTRACT EQUILIBRIUM moisture content-equilibrium relative humidity data for broken corn cobs have been determined for both desorption and adsorption conditions for three temperature levels and five moisture levels. The Modified Henderson and Chung equilibrium moisture equations have been fitted to these data by using non-linear regression procedures to estimate equation parameters. Both equations adequately represented the experimental data. A test of varietal differences indicated no significant difference in cob desorption ERH values for three selected corn varieties.

Desorption Equilibrium Moisture Relationships for Popcorn

ABSTRACT DESORPTION equilibrium moisture measurements were made for popcorn for five temperatures and seven moisture content levels. The data were found to differ from that given in ASAE D245.4. Parameter estimates were made for the Modified Henderson and for the Chung equation. The Chung equation gave a lower standard error for both moisture and relative humidity than did the Modified Henderson equation. Most of the difference in describing the data appeared to be for lower moisture and relative humidity values. Standard error and standard error as a percentage of the mean for both moisture and relative humidity was reduced for each equation when moisture was expressed on a wet rather than a dry basis.

A study of liquid-junction potentials in aqueous solutions

Due to the simultaneously unknown individual ion activity coefficients and liquid-junction potentials, a reasonable convention must be introduced defining the former in order to permit the calculation of the latter. The Guggenheim convention is analysed and chosen.Examples are reported of determination of potentials arising at junctions between concentrated strong acids and salt bridges. Liquid junction potentials set up between two concentrated strong acids at identical molalities are also considered, on the basis of a modified Henderson equation.